Question

If an article is sold for Rs.178 at a loss of 11%. What should be its selling price in order to earn a profit of 11%?
A. Rs.222.50
B. Rs.267
C. Rs.222
D. Rs.220

Answer 1

Hint: First of all, find out the cost price of the article by using the given data and the formula $$\text{C}\text{.P}={\displaystyle \frac{\text{S}\text{.P}}{100-\text{Loss\% }}}\times 100$$. Then find out the selling with a profit of 11% by using the formula $$\text{S}\text{.P}={\displaystyle \frac{100+\text{Profit\% }}{100}}\times \text{C}\text{.P}$$. So, use this concept to reach the solution of the given problem.

Complete step-by-step answer:
Given that the article is sold for Rs.178 at a loss of 11%.
So, selling price of article = Rs.178
Loss percent = 11%
We know that $$\text{C}\text{.P}={\displaystyle \frac{\text{S}\text{.P}}{100-\text{Loss\% }}}\times 100$$
So, cost price of the article $$={\displaystyle \frac{178}{100-11}}\times 100={\displaystyle \frac{178}{89}}\times 100=2\times 100=\text{Rs}.200$$
Now, we have to find the selling price of the article in order to get a profit of 11%
We know that, $$\text{S}\text{.P}={\displaystyle \frac{100+\text{Profit\% }}{100}}\times \text{C}\text{.P}$$
So, selling price of the article to have profit of 11% $$={\displaystyle \frac{100+11}{100}}\times 200$$
                                                                                           $$\begin{gathered} ={\displaystyle \frac{111\times 200}{100}} \\ =111\times 2 \\ =\text{Rs}\text{.222} \end{gathered}$$
Hence, to gain a profit of 11% the selling price should be Rs.222
Thus, the correct option is C. Rs.222

Note: There is a loss whenever the cost price of the article is greater than the selling price of the article. And there is a profit whenever the selling price of the article is greater than the cost price of the article.